An empirical study of the factor analysis stability hypothesis

Note is taken of four related sources of confusion as to the usefulness of Thurstone's factor analysis model and of their resolutions. One resolution uses Tucker's distinction between exploratory and confirmatory analyses. Eight analyses of two sets of data demonstrate the procedures and results of a confirmatory study with statistical tests of some, but not all, relevant hypotheses in an investigation of the stability (invariance) hypothesis. The empirical results provide estimates, as substitutes for unavailable sampling formulations, of effects of variation in diagonal values, in method of factoring, and in samples of cases. Implications of these results are discussed.The computational costs of this study were defrayed, in part, by a research small grant M-1922 from the National Institute of Health, and, in part, by support under project 176-0002 by the University of Iowa Computing Center, Dr. J. P. Dolch, Director. The assistance of Dr. Kern Dickman and Mr. Leonard Wevrick of the University of Illinois and of Mr. Norman Luther of the University of Iowa in handling the computing problems is gratefully acknowledged.     

An empirical application of confirmatory factor analysis to the multitrait-multimethod matrix

Though most social psychologists are aware of the use of factor analysis as an exploratory method to uncover latent dimensions, factor analysis can also be used in a confirmatory mode to test specific hypotheses. A confirmatory solution is unique and cannot be rotated. One possible use of confirmatory factor analysis is with the multitrait-multimethod matrix. Jaccard, Weber, and Lundmark's (1975) multitrait-multimethod matrix of two traits and four methods is analyzed using confirmatory factor analysis. Given the very small sample size the analysis is primarily illustrative. A simple two factor model with errors of measurement correlated across measures using the same method satisfactorily fits the data. Both discriminant and convergent validity are high and none of the methods has higher reliability or less correlated measurement error. The reliability of measures estimated by maximum likelihood factor analysis is lower than the test-retest reliability since method variance is subtracted out. Confirmatory factor analysis is recommended over the Campbell-Fiske criteria.     

An iterative procedure for extracting skill maps from data

The methodologies for the construction of a knowledge structure mainly refer to the query to experts, the skill maps, and the data-driven approaches. This last method is of growing interest in recent literature. In this paper, an iterative procedure for building a skill map from a set of data is introduced. This procedure is based on the minimization of the distance between the knowledge structure delineated by a given skill map and the data. The accuracy of the proposed method is tested through a number of simulation studies where the amount of noise in the data is manipulated as well as the kind of structure to be reconstructed. Results show that the procedure is accurate and that its performance tends to be sufficiently stable even with high error rates. The procedure is compared to two already-existing methodologies to derive knowledge structures from a set of data. The use of the corrected Akaike Information Criterion (AICc) as a stopping criterion of the iterative reconstruction procedure is tested against the app criterion introduced by Schrepp. Moreover, two empirical applications on clinical data are reported, and their results show the applicability of the procedure.     

An SAS/IML procedure for maximum likelihood factor analysis

Maximum likelihood factor analysis (MLFA), originally introduced by Lawley (1940), is based on a firm mathematical foundation that allows hypothesis testing when normality is assumed with large sample sizes. MLFA has gained in popularity since Jöreskog (1967) implemented an iterative algorithm to estimate parameters. This article presents a concise program using matrix language SAS/LML with the optimization subroutine NLPQN to obtain MLFA solutions. The program is pedagogically useful because it shows the step-by-step computational processes for MLFA, whereas almost all other statistical packages for MLFA are in “black boxes.” It is also demonstrated that this approach can be extended to other multivariate methods requiring numerical optimizations, such as the widely used structural equation modeling. Researchers may find this program useful in conducting Monte Carlo simulation studies to investigate the properties of multivariate methods that involve numerical optimizations.     

An empirical investigation of the factor structure of the AUDIT

This study investigated the Alcohol Use Disorders Identification Test's (AUDIT) factor structure and psychometric properties. The factor structure was derived from a sample of 7,035 men and women primary care patients. A principal components analysis identified 2 factors in the AUDIT data and was supported in a confirmatory factor analysis (CFA). The 2 factors were Dependence/Consequences and Alcohol Consumption. The CFA also provided support for a 3-factor model whose factors (Alcohol Consumption, Alcohol Dependence, and Related Consequences) matched those proposed by the AUDIT's developers. Psychometric indexes were determined by use of the baseline and 12-month follow-up data of 301 men and women who entered a clinical trial. The results showed that the 2 factors had good reliability. Validity tests supported the interpretation of what the 2 factors measure, its implications for relationships to other variables, and the comparability of the 2- and 3-factor models.     

An empirical analysis of the super-latent inhibition effect

In three conditioned taste aversion experiments, we examined the roles of several variables in producing super-latent inhibition (LI). This effect, greater LI after a long interval than after a short interval between the conditioning and the test stages (De la Casa & Lubow, 2000), was shown to increase with the number of stimulus preexposures (0, 2, or 4; Experiment 1) and with the length of the delay interval (1, 7, 14, or 21 days; Experiment 2). Furthermore, super-LI was obtained when the delay interval was introduced between the conditioning and the test stages (Experiments 1 and 2), but not when it was introduced between the preexposure and the conditioning stages (Experiment 3). The results are discussed in relation to interference explanations of LI.     

Robustness of the maximum-likelihood estimation procedure in factor analysis

In order to determine the robustness of the maximum-likelihood estimation procedure, random variates from six distributions were generated independently on a high speed computer and then used to represent the common and specific factors in a factor analysis model in which the coefficients of these factors had been specified. Using Lawley's approximatex ² statistic in evaluating the estimates obtained, the estimation procedure is found to be insensitive to changes in the distributions considered.This study was conducted while the authors were members of the Statistical Laboratory at Iowa State University. All computations were done at Iowa State on an IBM 7074.     

The production and verification tasks in mental addition: An empirical comparison

We respond to A. Baroody's comment (1984, Developmental Review, 4, 148–156) with an empirical comparison of the production and verification tasks. With the exception of performance at the first grade level, the two tasks yield essentially identical conclusions. The results of an adjunct task, in which the rate of mental counting was assessed, suggest that children as young as second grade are relying on memory retrieval to a significant degree. In contrast to Baroody's speculation, there appear to be no widespread difficulties associated with results from the verification task. Furthermore, the task permits a more analytic examination of performance and underlying mental process than is afforded by the production task. We conclude by reiterating the empirical support for a model of fact retrieval, and suggesting that accessibility of the arithmetic facts is the basic factor which underlies both fact retrieval and procedural knowledge performance.     

An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data

Confirmatory factor analysis (CFA) is widely used for examining hypothesized relations among ordinal variables (e.g., Likert-type items). A theoretically appropriate method fits the CFA model to polychoric correlations using either weighted least squares (WLS) or robust WLS. Importantly, this approach assumes that a continuous, normal latent process determines each observed variable. The extent to which violations of this assumption undermine CFA estimation is not well-known. In this article, the authors empirically study this issue using a computer simulation study. The results suggest that estimation of polychoric correlations is robust to modest violations of underlying normality. Further, WLS performed adequately only at the largest sample size but led to substantial estimation difficulties with smaller samples. Finally, robust WLS performed well across all conditions.     

A simple procedure for approximate factor analysis

A variation of the centroid method is described and illustrated. By the application of new rules for reflecting signs, it may be possible to reduce to insignificance the factor loadings of tests showing insignificant correlation (original or residual) with clusters of tests having relatively high intercorrelations. As a result, a factor common to any one of these clusters may be revealed by the centroid method itself with little or no need for rotation of axes or further calculations.     

Obtaining maximum-likelihood estimates of factor loadings and communalities using an easily implemented iterative computer procedure

This paper considers the problem of computing estimates of factor loadings, specific variances, and communalities for a factor analytic model. The equations for maximum-likelihood estimators are discussed. Iterative formulas are developed to solve the maximum-likelihood equations and a simple and efficient method of implementation on a digital computer is described. Use of the iterative formulas and computing techniques for other estimators of factor loadings and communalities is also considered to provide a very general approach for this aspect of factor analysis.     

An empirical study of the validity of handwriting analysis

The EPQ was administered to 99 Ss, and a handwriting sample provided by each. A professional graphologist undertook to analyse the handwritings, and fill in the EPQ as she thought would have been done by the respondents. Significant correlations were only obtained for the P category; neither E, nor N, nor the L scale showed significant correlations between Ss and the graphologist.     

An empirical analysis of trends in psychology

The present research examined trends in the prominence of 4 widely recognized schools in scientific psychology: psychoanalysis, behaviorism, cognitive psychology, and neuroscience. The results, which replicated across 3 measures of prominence, showed the following trends: (a) psychoanalytic research has been virtually ignored by mainstream scientific psychology over the past several decades; (b) behavioral psychology has declined in prominence and gave way to the ascension of cognitive psychology during the 1970s; (c) cognitive psychology has sustained a steady upward trajectory and continues to be the most prominent school; and (d) neuroscience has seen only a modest increase in prominence in mainstream psychology, despite evidence for its conspicuous growth in general. The authors use these findings as a springboard for discussing different views of scientific prominence and conclude that psychologists should evaluate trends in the field empirically, not intuitively.     

An empirical test of the covariation analysis in causal attribution

The present investigation was designed to reveal the cognitive inference processes associated with both detection and utilization of covariation information in causal attribution. Male undergraduates were (a) informed that a test was easy or difficult and shown a videotape in which (b) the test-taker's performance was high or low, and (c) covariation between the test-taker's effort expenditure and trial-by-trial outcome was present or absent. High performance was attributed to the test-taker's effort and ability, whereas low performance was attributed to the difficulty of the test. However, recognition of the covariance relationship decreased the attribution of high performance to ability and of low performance to test difficulty and increased the attribution of low performance to effort. Effort attribution in the high performance condition was independent of covariation information. The results are discussed in terms of the relationship between covariation information and typical beliefs about the causes of achievement outcomes.     

Selection of variables in exploratory factor analysis: An empirical comparison of a stepwise and traditional approach

The purpose of this study was to investigate and compare the performance of a stepwise variable selection algorithm to traditional exploratory factor analysis. The Monte Carlo study included six factors in the design; the number of common factors; the number of variables explained by the common factors; the magnitude of factor loadings; the number of variables not explained by the common factors; the type of anomaly evidenced by the poorly explained variables; and sample size. The performance of the methods was evaluated in terms of selection and pattern accuracy, and bias and root mean squared error of the structure coefficients. Results indicate that the stepwise algorithm was generally ineffective at excluding anomalous variables from the factor model. The poor selection accuracy of the stepwise approach suggests that it should be avoided.     

An empirical analysis of lay conceptions of memory domains

Although experts consider memory in terms of different domains (e.g., short-term memory, spatial memory), little is known about the way in which lay people conceive memory domains. Study 1 addressed this issue by asking 79 French lay people to group together 125 memory situations (previously generated by lay people) according to their similarity. Study 2 used a similar procedure with 99 American lay people and 40 different memory situations. Hierarchical cluster analyses revealed five main memory domains common to the two studies: learn a set of things and recall them later, episodic and detailed memory, autobiographical memory, memory for day-to-day living, and failure to remember. Study 1 revealed a further domain: memory for intellectual and exact knowledge. Identifying these shared lay conceptions of memory provides insights into how lay people communicate about memory and will enable the construction of memory self-evaluation measures that are more representative of all memory domains.     

Deviance and the neutralization of moral commitment: An empirical analysis

Neutralization theory was proposed by Sykes and Matza (1957) as a theory of juvenile delinquency. Its major propositions are: (1) Delinquents maintain moral commitment to conventional norms, and (2) the ability to neutralize moral commitment facilitates juvenile delinquency. The present research attempts to evaluate neutralization theory for predicting variation in self‐reported expected illegal behavior in a random sample of 350 adults. Data analysis indicates that (1) neutralization is conceptually and empirically distinct from moral commitment, and (2) the interaction between moral commitment and neutralization significantly explains expected involvement in future deviance.     

A new iterative method for correcting erroneous communality estimates in factor analysis

A new method for correcting erroneous communality estimates is applicable to any completed orthogonal factor solution. It seeks, by direct correction of factor loadings, to make the residuals conform to the chance error criteria of zero mean and zero skewness for each row separately. Two numerical examples, with one and two factors, respectively, are presented. The method can be used as a short cut for Dwyer's extension in adding variables to a matrix. It can also be used as a short cut in cross-validation factor studies. Successful use on problems with many variables and numerous factors is claimed. Factors can be made oblique,after correction, if desired.